Chaos is aperiodic long-term behavior in a deterministic system that exhibits sensitive dependence on initial conditions. No definition of the term chaos is universally accepted yet, but almost everyone would agree on those properties. The term attractor is also difficult to define in a rigorous way. We want a definition that is broad enough to include all the natural candidates, but restrictive enough to exclude the imposters. There is still disagreement about what the exact definition should be. And what's a "strange attractor", like in the Lorenz equations?
► Next, exploring the Lorenz system parameter space & bifurcation diagram
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► Lorenz equations
Derivation and chaotic waterwheel • 3D Systems, Lorenz Equ...
Volume contraction and symmetry • Lorenz Equations Prope...
Fixed point analysis • Lorenz Equations Fixed...
Deducing the Lorenz attractor • Lorenz Attractor- How ...
► Additional background
Lyapunov exponents to quantify chaos • Lyapunov Exponents & S...
Pitchfork bifurcations of fixed points • Bifurcations Part 3- P...
Hopf bifurcations, unstable limit cycles • Bifurcations in 2D, Pa...
Quasiperiodic motion on a torus • Coupled Oscillators, Q...
Trapping region, Poincaré-Bendixson • Limit Cycles, Part 3: ...
► Advanced lecture on the center manifold of the origin in the Lorenz system
• Center Manifolds Depen...
► From 'Nonlinear Dynamics and Chaos' (online course).
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References:
Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 9: Lorenz Equations
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27 сен 2024
